Question

Solve the triangle, if possible. Determine the number of possible solutions. A = 76.6° a = 11.3 b = 9.8 Select the correct choice below and fill in the answer boxes within the choice. (Round to the nearest tenth as needed.) O A. There is only 1 possible solution for the triangle. The measurements for the remaining angles A and C and side c are as follows. mZB= mZC = The length of side c= B. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. mZB = mZC = The length of side c= The measurements for the solution with the shorter side c are as follows. mZB= mZC= The length of side c= O C. There are no possible solutions for the triangle.

Answer 1

Son Griven that A= 76.6 a = 11.3 b = 9.8 > using Sine stuk. a b с Sina SinB Sinc 11:3 9.8 Sint.) SinB SinB = 9.8 Sin 46.63 11-3 SinB = 0.84364 B- Sin (0.84364) B=57.5 O we Know Sum of angle of Sum of angle of a triangle teriangle is 180 A + B + c = 180° 76.6 +57-5 toa 180 180 1361 C = 43.99

Also, a Sin A 느 Sinc { By Sine wrude C 11.3 Sin (76.6) Sin143.9°) C 11:3 Sin (43.9 Sin(+6-6) 8.1 Hence Solution are 43.g? 1 MLB = (57-5 mLC The length of shorter side c=18.1